CCF: Small: Quantum Algorithms for Constructing Ground and Gibbs States

This project aims to develop new algorithms that enable quantum computers to prepare the natural states of quantum systems, which are essential for understanding materials, chemistry, and many physical phenomena. In particular, it focuses on efficiently generating ground states, which capture a system’s lowest-energy behavior, and thermal (Gibbs) states, which describe systems at realistic temperatures. Although recent advances have shown that such state preparation is possible in principle, it remains unclear when these methods can be made practical. This work seeks to clarify those conditions, improve algorithmic performance, and adapt these techniques for both future large-scale quantum computers and the more limited devices available today. By advancing our ability to simulate quantum systems, this project has the potential to impact fields ranging from materials design to fundamental physics, while also contributing to the training of students in quantum computing. This project develops and analyzes quantum algorithms for preparing ground and Gibbs states of local Hamiltonians, with a focus on dissipative (Lindbladian) methods. The central goal of this work is to determine when recently proposed quantum Gibbs sampling algorithms converge efficiently, and to extend these guarantees to broader classes of systems and temperature regimes, including both fault-tolerant and near-term (NISQ) settings. The approach combines tools from quantum information, spectral analysis, and classical Markov chain theory to study convergence and mixing behavior, including the role of Hamiltonian structure, jump operators, and initial states. The project also explores simplified, noise-resilient implementations suitable for near-term devices and investigates extensions to ground state preparation inspired by classical techniques such as tensor networks. The goals of the project include establishing new convergence guarantees for quantum Gibbs sampling and developing practical implementations on emerging quantum hardware. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2533522 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Sandra Irani | Institution: University of California-Irvine, IRVINE, CA | Award Amount: $600,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2533522 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2533522.html